1. Field of the Invention
The present invention is directed to a method for imaging with nuclear magnetic resonance given a k-space trajectory proceeding on a curve.
2. Description of the Prior Art
For image generation with nuclear magnetic resonance, magnetic resonance signals are spatially encoded with magnetic gradient fields before and during their reception. The spatial encoding means that k-space is occupied with signals, k-space being defined via the time integral of the gradient fields. The signals in k-space are then subjected to a Fourier transformation whose result is supplied to an image presentation. In certain fast pulse sequences, particularly given the echo-planar method, the gradient fields are additionally rapidly switched during the reception of the magnetic resonance signals. For example, the amplitude of a first gradient field is sinusoidally modified given a constant amplitude of a further gradient field whose gradient is aligned perpendicular to the gradient of the first gradient field. A sinusoidal signal occupancy thus occurs in the k-space.
European Application 0 076 054 discloses a method for imaging with nuclear magnetic resonance using the echo-planar sequences wherein sinusoidal gradients are employed. In order to avoid image distortions, the sampling of the received magnetic resonance signals ensues equidistantly in k-space. This corresponds to a non-equidistant sampling of the received magnetic resonance signals in the time domain. Since the sampling must ensue on a serpentine-like trajectory along the lines of the Cartesian k-space grid, the fastest possible sampling of k-space cannot be achieved. Other properties such as, for example, the motion sensitivity thus are also essentially defined.
German OS 40 03 547 discloses how the image information can be distortion-corrected by a sampling with a constant sampling rate in the time domain. The constant sampling rate denotes a non-equidistant occupancy of k-space with signals given a sinusoidal trajectory in k-space. The non-equidistant signals are then imaged onto a rectangular grid by an interpolation. The following Fourier transformation then yields image data for a non-distorted presentation. The sampling of the received magnetic resonance signal must allow the sampling theorem to be satisfied for the highest frequency to be sampled. Given the constant sampling rate employed, however, this means that other regions of the magnetic resonance signal are highly over-sampled.
An object of the present invention is to provide a method for imaging with magnetic resonance wherein the reconstruction of the image data from the received magnetic resonance signals can be implemented with reduced outlay.
The object is achieved with the following method steps: Magnetic resonance signals are read out under the influence of a magnetic gradient field with the direction of a gradient of the gradient field being modified during the reception, so that the k-space trajectory proceeds on a curve. The magnetic resonance signals are sampled with a variable sampling rate and the samples are digitized. The sampling rate is varied such that an occupation density of k-space with samples is essentially uniform. The inventive method yields a two-fold advantage in view of the outlay for the reconstruction of the image data. First, the variable sampling rate makes it possible always to optimally implement a sampling that satisfies the sampling theorem, so that substantially fewer raw data are generated compared to a constant sampling. However, the samples do not yet lie on a rectangular grid, so that interpolation data must still be generated with an interpolation procedure. Due to the uniform occupancy of k-space with samples that has ensued as a result of the same sampling density, a sampling density correction is not required and a processing step is thereby eliminated. This is true for 2D as well as 3D trajectories wherein the gradient amplitudes are varied during the reception phase (readout), for example given rosette-shaped sampling (Lissajou figure trajectory) or given projection sampling. More general sampling trajectories such as, for example, Archimedean spirals yield shorter sampling times with a given gradient power (amplitude and rise time) and have a more beneficial motion susceptibility. These trajectories, however, do not traverse the grid points of the Cartesian k-space grid.
In an embodiment, the k-space trajectory proceeds helically. The middle of the k-space is thereby sampled first, his defining the contrast in the imaging. Important image information in the imaging of rapidly changing events thus can be acquired first.
In another embodiment, the interpolation is implemented as sinc interpolation. This interpolation can be implemented especially simply when k-space is occupied with identical sampling density. Values of the sinc function weighted with the corresponding samples that arise at the grid points are added and thus yield the interpolation values.